Question

 Cho 𝑥 + 1 /𝑥 = 3. Tính 𝑥 ^3 + 1/ 𝑥 ^3

Answer 1

\(\dfrac{x+1}{x}=3\Leftrightarrow x+1=3x\Leftrightarrow x=\dfrac{1}{2}\\ \dfrac{x^3+1}{x^3}=\dfrac{\dfrac{1}{8}+1}{\dfrac{1}{8}}=\dfrac{9}{8}\cdot8=9\)

Answer 2

\(x^3+\dfrac{1}{x^3}=\left(x+\dfrac{1}{x}\right)^3-3x\cdot\dfrac{1}{x}\left(x+\dfrac{1}{x}\right)=3^3-3\cdot3=27-9=18\)